Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/9903266

The magnetic susceptibility of disordered non-diffusive mesoscopic systems

Edward McCann·Klaus Richter
View original source ↗Read source document ↗Export metadata ↓

Abstract

Disorder-induced spectral correlations of mesoscopic quantum systems in the non-diffusive regime and their effect on the magnetic susceptibility are studied. We perform impurity averaging for non-translational invariant systems by combining a diagrammatic perturbative approach with semiclassical techniques. This allows us to study the entire range from clean to diffusive systems. As an application we consider the magnetic response of non-interacting electrons in microstructures in the presence of weak disorder. We show that in the ballistic case (elastic mean free path $\ell$ larger than the system size) there exist two distinct regimes of behaviour depending on the relative magnitudes of $\ell$ and an inelastic scattering length $L_ϕ$. We present numerical results for square billiards and derive approximate analytical results for generic chaotic geometries. The magnetic field dependence and $L_ϕ$ dependence of the disorder-induced susceptibility is qualitatively similar in both types of geometry.

Explore related subjects

cond-mat.mes-hall

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Edward McCann, Klaus Richter. 1999-03-17. The magnetic susceptibility of disordered non-diffusive mesoscopic systems. https://doi.org/10.1103/physrevb.59.13026

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Gapped out-of-phase plasmon modes in alternating-twist multilayer graphene

We theoretically investigate the plasmon modes of alternating-twist multilayer graphene. In multilayer systems, interlayer coupling gives rise to distinctive plasmon modes, but calculations in moiré systems remain challenging due to their complex tunneling structures. Using the Kac-Murdock-Szegő Toeplitz formalism, we derive that the in-phase mode exhibits the conventional $\sqrt{q}$ behavior, while the out-of-phase modes acquire plasmon gaps determined by specific interband transitions between Dirac cones with different velocities in the long-wavelength limit. We demonstrate that these out-of-phase modes remain undamped in the weak Coulomb-interaction limit when the twist angle exceeds a critical value ($θ\gtrsim 2.75^\circ$ for the alternating-twist trilayer case), regardless of the carrier density as long as the low-energy effective Dirac Hamiltonian remains valid. Furthermore, we consider the effect of a perpendicular electric field, and demonstrate how plasmon modes can be tuned by a gate voltage.

cond-mat.mes-hall↗
arXiv2026

Optical properties of hydrogenated graphene superlattices

We investigate with first principles theoretical methods optical response accounting for excitonic effects of quasi-one dimensional monolithic arrays of graphene nanostripes -- two-dimensional graphene superlattices, where quasi-metallic and dielectric regions alternate by selective hydrogenation of graphene. It is shown that chemical engineering of the graphene surface can lead to strong and well-isolated absorption peaks in the far-infrared and possibly even terahertz frequencies. The band gap scaling suggests no excitonic insulators.

cond-mat.mes-hall↗
arXiv2026

Long-lived Laughlin pairs in a depleted quantum Hall edge channel

On-demand sources and mesoscopic beam splitters allow individual ballistic electrons to collide in depleted quantum Hall edge channels, where their unscreened Coulomb interaction acts as a strong, controllable nonlinearity. Theory suggests a more striking possibility: in a strong magnetic field, the same repulsion can drive quantized relative circulation, allowing two electrons to propagate together as a positive-energy Laughlin pair. The relevance of such pairs to experiment depends on lifetimes in realistic guiding potentials and on whether the proposed collision pathway to pair formation survives full two-dimensional dynamics. We develop a microscopic theory of quasibound Laughlin pairs using the physical two-electron Hamiltonian. For a general local electric-field gradient, we determine the dissociation threshold, number of quasibound states, and decay rates. Complex scaling and analytic tunneling theory show that lifetimes grow exponentially with pair energy above threshold. Applied to reported GaAs parameters, the theory indicates that existing devices may already support the lowest spin-polarized pair, with a lifetime estimate roughly two orders of magnitude longer than typical propagation times. We simulate a collision with the full finite-field Hamiltonian, providing both a framework for nonlinear two-electron quantum dynamics and evidence for Laughlin-pair formation in a representative two-electron collision. We use Husimi distributions and their zeros to visualize both quasibound resonances and transient collision states in phase space. These results place the preparation, propagation, and detection of repulsively paired electrons within reach of existing single-electron circuit technology. They identify kinematic stabilization under constrained one-dimensional propagation as a pairing mechanism that may extend to anyonic quantum Hall edge excitations.

cond-mat.mes-hall↗